The big downside of putting all 7 passengers on one reservation is that it may cost more than booking 7 single flights. This is because all passengers on a shared UA PNR need to have the same fare class, and fare class availability on the cheapest available tickets is often published with fewer than 7 open seats in the cheapest available bucket.

Suppose a flight you're looking at has inventory like, say,
F6 A6 JN6 Z5 ZN5 P5 PN5 R4 RN4 IN0 I0 Y9 YN9 B9 M9 E9 U9 H9 HN9 Q9 V9 W9 S6 T0 L0 K0 G0 N0 XN0 X0

And suppose there is a $500 W fare and a $100 S fare posted valid on that itinerary.

Then if you book a single 7-passenger itinerary it'll book into W (costing $3500) because all passengers on a PNR need to be booked in exactly the same fare class (this is a common technical limitation that has applies to, e.g., all multi-passenger PNRs I have ever seen on an airline).

But if in this hypothetical scenario you book one 4-passenger itinerary, probably that will book into S (costing $400 and leaving S2) and if you then book a 3-passenger itinerary, probably that will book into W (costing $1500).

So — check carefully whether you're losing money by unnecessarily booking into a higher than needed fare class with a reservation with a large number of passengers.